Lebwohl-Lasher model: Difference between revisions
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The '''Lebwohl-Lasher model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase | nematic liquid crystal]]. The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase|nematogenic]] particles with the [[Intermolecular pair potential | pair potential]] | The '''Lebwohl-Lasher model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase | nematic liquid crystal]] | ||
<ref>[http://dx.doi.org/10.1103/PhysRevA.6.426 P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A '''6''' pp. 426 - 429 (1972)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.7.2222.3 Erratum, Physical Review A '''7''' p. 2222 (1973)]</ref>. | |||
The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase|nematogenic]] particles with the [[Intermolecular pair potential | pair potential]] | |||
:<math>\Phi_{ij} = -\epsilon_{ij} P_2 (\cos \beta_{ij}) </math> | :<math>\Phi_{ij} = -\epsilon_{ij} P_2 (\cos \beta_{ij}) </math> | ||
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where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials |Legendre polynomial]]. | where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials |Legendre polynomial]]. | ||
==Isotropic-nematic transition== | ==Isotropic-nematic transition== | ||
( | <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> | ||
:<math>T^*_{NI^*}= \frac{k_BT_{NI}}{\epsilon}=1.1201 \pm 0.0006</math> | :<math>T^*_{NI^*}= \frac{k_BT_{NI}}{\epsilon}=1.1201 \pm 0.0006</math> | ||
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The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. | The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. | ||
This system exhibits a [[Kosterlitz-Thouless transition|Kosterlitz-Touless]] continuous transition | This system exhibits a [[Kosterlitz-Thouless transition|Kosterlitz-Touless]] continuous transition | ||
<ref>Mondal, Roy; Physics Letters A, 2003, 312, 397-410</ref> | |||
<ref>Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311</ref>. | |||
==Lattice Gas Lebwohl-Lasher model== | ==Lattice Gas Lebwohl-Lasher model== | ||
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between nearest-neighbour particles is that of the Lebwohl-Lasher model. | between nearest-neighbour particles is that of the Lebwohl-Lasher model. | ||
This model has been studied in | This model has been studied in | ||
<ref>Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702</ref>. | |||
Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702 | |||
==References== | ==References== | ||
<references/> | |||
[[category: models]] | [[category: models]] | ||
[[category: liquid crystals]] | [[category: liquid crystals]] | ||
Revision as of 15:26, 19 February 2009
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The Lebwohl-Lasher model is a lattice version of the Maier-Saupe mean field model of a nematic liquid crystal [1][2]. The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial nematogenic particles with the pair potential
where , is the angle between the axes of nearest neighbour particles and , and is a second order Legendre polynomial.
Isotropic-nematic transition
Planar Lebwohl–Lasher model
The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. This system exhibits a Kosterlitz-Touless continuous transition [4] [5].
Lattice Gas Lebwohl-Lasher model
This model is the lattice gas version of the Lebwohl-Lasher model. In this case the sites of the lattice can be occupied by particles or empty. The interaction between nearest-neighbour particles is that of the Lebwohl-Lasher model. This model has been studied in [6].
References
- ↑ P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A 6 pp. 426 - 429 (1972)
- ↑ Erratum, Physical Review A 7 p. 2222 (1973)
- ↑ U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 58 (1986)
- ↑ Mondal, Roy; Physics Letters A, 2003, 312, 397-410
- ↑ Chiccoli, C.; Pasini, P. & Zannoni, C., Physica, 1988, 148A, 298-311
- ↑ Bates, M. A., Computer simulation study of the phase behavior of a nematogenic lattice-gas model, Phys. Rev. E, 2001, 64, 051702